LMFDB - Embedded newform 378.3.n.c.325.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,3,Mod(271,378)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("378.271");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 13 x^{10} - 10 x^{9} + 89 x^{8} - 70 x^{7} + 314 x^{6} - 138 x^{5} + 673 x^{4} + \cdots + 49 $ x^12 - 2x^11 + 13x^10 - 10x^9 + 89x^8 - 70x^7 + 314x^6 - 138x^5 + 673x^4 - 284x^3 + 716x^2 + 168*x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			325.5
Root			$0.791791 + 1.37142i$ of defining polynomial
Character	$\chi$	$=$	378.325
Dual form			378.3.n.c.271.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.200623 - 0.115830i) q^{5} +(6.91963 - 1.05770i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.200623 - 0.115830i) q^{5} +(6.91963 - 1.05770i) q^{7} -2.82843 q^{8} +(0.283724 + 0.163808i) q^{10} +(9.77891 - 16.9376i) q^{11} +10.4307i q^{13} +(6.18833 + 7.72687i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(17.0529 + 9.84551i) q^{17} +(6.48236 - 3.74259i) q^{19} +0.463320i q^{20} +27.6589 q^{22} +(-2.69961 - 4.67587i) q^{23} +(-12.4732 + 21.6042i) q^{25} +(-12.7750 + 7.37564i) q^{26} +(-5.08764 + 13.0428i) q^{28} -8.56771 q^{29} +(37.7135 + 21.7739i) q^{31} +(2.82843 - 4.89898i) q^{32} +27.8473i q^{34} +(1.26573 - 1.01370i) q^{35} +(29.4042 + 50.9296i) q^{37} +(9.16744 + 5.29282i) q^{38} +(-0.567448 + 0.327616i) q^{40} -69.6222i q^{41} -10.7881 q^{43} +(19.5578 + 33.8752i) q^{44} +(3.81783 - 6.61267i) q^{46} +(7.76832 - 4.48504i) q^{47} +(46.7625 - 14.6378i) q^{49} -35.2794 q^{50} +(-18.0666 - 10.4307i) q^{52} +(-30.8209 + 53.3834i) q^{53} -4.53076i q^{55} +(-19.5717 + 2.99162i) q^{56} +(-6.05829 - 10.4933i) q^{58} +(-29.8476 - 17.2325i) q^{59} +(58.8187 - 33.9590i) q^{61} +61.5860i q^{62} +8.00000 q^{64} +(1.20819 + 2.09265i) q^{65} +(-36.5287 + 63.2696i) q^{67} +(-34.1058 + 19.6910i) q^{68} +(2.13653 + 0.833397i) q^{70} +2.57953 q^{71} +(-116.231 - 67.1059i) q^{73} +(-41.5838 + 72.0253i) q^{74} +14.9704i q^{76} +(49.7516 - 127.545i) q^{77} +(-47.1107 - 81.5982i) q^{79} +(-0.802493 - 0.463320i) q^{80} +(85.2695 - 49.2304i) q^{82} -66.7610i q^{83} +4.56162 q^{85} +(-7.62837 - 13.2127i) q^{86} +(-27.6589 + 47.9067i) q^{88} +(37.4365 - 21.6140i) q^{89} +(11.0326 + 72.1768i) q^{91} +10.7984 q^{92} +(10.9861 + 6.34281i) q^{94} +(0.867008 - 1.50170i) q^{95} -13.8343i q^{97} +(50.9936 + 46.9217i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 6 q^{5}+O(q^{10}) $ 12 * q - 12 * q^4 - 6 * q^5	$ 12 q - 12 q^{4} - 6 q^{5} - 12 q^{10} + 6 q^{11} - 12 q^{14} - 24 q^{16} + 24 q^{17} - 30 q^{19} + 96 q^{23} + 36 q^{25} - 48 q^{26} + 24 q^{28} - 108 q^{29} + 36 q^{31} + 108 q^{35} - 12 q^{37} + 96 q^{38} + 24 q^{40} - 156 q^{43} + 12 q^{44} + 48 q^{46} - 42 q^{47} - 108 q^{49} - 336 q^{50} + 48 q^{52} - 60 q^{53} + 24 q^{56} + 12 q^{58} + 66 q^{59} + 186 q^{61} + 96 q^{64} + 180 q^{65} - 156 q^{67} - 48 q^{68} - 72 q^{70} - 372 q^{71} - 366 q^{73} + 24 q^{74} + 534 q^{77} + 84 q^{79} + 24 q^{80} - 192 q^{82} + 276 q^{85} + 12 q^{86} + 306 q^{89} + 390 q^{91} - 384 q^{92} + 24 q^{94} - 420 q^{95} + 216 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 - 6 * q^5 - 12 * q^10 + 6 * q^11 - 12 * q^14 - 24 * q^16 + 24 * q^17 - 30 * q^19 + 96 * q^23 + 36 * q^25 - 48 * q^26 + 24 * q^28 - 108 * q^29 + 36 * q^31 + 108 * q^35 - 12 * q^37 + 96 * q^38 + 24 * q^40 - 156 * q^43 + 12 * q^44 + 48 * q^46 - 42 * q^47 - 108 * q^49 - 336 * q^50 + 48 * q^52 - 60 * q^53 + 24 * q^56 + 12 * q^58 + 66 * q^59 + 186 * q^61 + 96 * q^64 + 180 * q^65 - 156 * q^67 - 48 * q^68 - 72 * q^70 - 372 * q^71 - 366 * q^73 + 24 * q^74 + 534 * q^77 + 84 * q^79 + 24 * q^80 - 192 * q^82 + 276 * q^85 + 12 * q^86 + 306 * q^89 + 390 * q^91 - 384 * q^92 + 24 * q^94 - 420 * q^95 + 216 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	0.200623	−	0.115830i	0.0401247	−	0.0231660i	−0.479803	−	0.877376i	$-0.659292\pi$
$5$	0.200623	−	0.115830i	0.0401247	−	0.0231660i	0.519928	+	0.854210i	$0.325959\pi$
$6$		0			0
$7$	6.91963	−	1.05770i	0.988519	−	0.151100i
$7$	6.91963	−	1.05770i	0.988519	−	0.151100i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	0.283724	+	0.163808i	0.0283724	+	0.0163808i
$11$	9.77891	−	16.9376i	0.888992	−	1.53978i	0.0479239	−	0.998851i	$-0.484740\pi$
$11$	9.77891	−	16.9376i	0.888992	−	1.53978i	0.841068	−	0.540929i	$-0.181927\pi$
$12$		0			0
$13$			10.4307i			0.802364i	0.915998	+	0.401182i	$0.131401\pi$
$13$			10.4307i			0.802364i	−0.915998	+	0.401182i	$0.868599\pi$
$14$	6.18833	+	7.72687i	0.442023	+	0.551920i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	17.0529	+	9.84551i	1.00311	+	0.579148i	0.909168	−	0.416430i	$-0.136719\pi$
$17$	17.0529	+	9.84551i	1.00311	+	0.579148i	0.0939453	+	0.995577i	$0.470052\pi$
$18$		0			0
$19$	6.48236	−	3.74259i	0.341177	−	0.196979i	−0.319615	−	0.947547i	$-0.603554\pi$
$19$	6.48236	−	3.74259i	0.341177	−	0.196979i	0.660792	+	0.750569i	$0.270220\pi$
$20$			0.463320i			0.0231660i
$21$		0			0
$22$	27.6589			1.25722
$23$	−2.69961	−	4.67587i	−0.117374	−	0.203298i	0.801352	−	0.598193i	$-0.204114\pi$
$23$	−2.69961	−	4.67587i	−0.117374	−	0.203298i	−0.918726	+	0.394895i	$0.870781\pi$
$24$		0			0
$25$	−12.4732	+	21.6042i	−0.498927	+	0.864166i
$26$	−12.7750	+	7.37564i	−0.491346	+	0.283679i
$27$		0			0
$28$	−5.08764	+	13.0428i	−0.181701	+	0.465816i
$29$	−8.56771			−0.295438			−0.147719	−	0.989029i	$-0.547193\pi$
$29$	−8.56771			−0.295438			−0.147719	+	0.989029i	$0.547193\pi$
$30$		0			0
$31$	37.7135	+	21.7739i	1.21657	+	0.702385i	0.964182	−	0.265242i	$-0.0854520\pi$
$31$	37.7135	+	21.7739i	1.21657	+	0.702385i	0.252384	+	0.967627i	$0.418785\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$			27.8473i			0.819038i
$35$	1.26573	−	1.01370i	0.0361636	−	0.0289628i
$36$		0			0
$37$	29.4042	+	50.9296i	0.794708	+	1.37647i	0.923024	+	0.384741i	$0.125709\pi$
$37$	29.4042	+	50.9296i	0.794708	+	1.37647i	−0.128317	+	0.991733i	$0.540957\pi$
$38$	9.16744	+	5.29282i	0.241248	+	0.139285i
$39$		0			0
$40$	−0.567448	+	0.327616i	−0.0141862	+	0.00819041i
$41$		−	69.6222i		−	1.69810i	−0.528310	−	0.849052i	$-0.677174\pi$
$41$		−	69.6222i		−	1.69810i	0.528310	−	0.849052i	$-0.322826\pi$
$42$		0			0
$43$	−10.7881			−0.250887			−0.125444	−	0.992101i	$-0.540035\pi$
$43$	−10.7881			−0.250887			−0.125444	+	0.992101i	$0.540035\pi$
$44$	19.5578	+	33.8752i	0.444496	+	0.769890i
$45$		0			0
$46$	3.81783	−	6.61267i	0.0829963	−	0.143754i
$47$	7.76832	−	4.48504i	0.165283	−	0.0954265i	−0.415076	−	0.909787i	$-0.636245\pi$
$47$	7.76832	−	4.48504i	0.165283	−	0.0954265i	0.580360	+	0.814360i	$0.302912\pi$
$48$		0			0
$49$	46.7625	−	14.6378i	0.954338	−	0.298730i
$50$	−35.2794			−0.705589
$51$		0			0
$52$	−18.0666	−	10.4307i	−0.347434	−	0.200591i
$53$	−30.8209	+	53.3834i	−0.581526	+	1.00723i	0.413772	+	0.910380i	$0.364211\pi$
$53$	−30.8209	+	53.3834i	−0.581526	+	1.00723i	−0.995299	+	0.0968528i	$0.969122\pi$
$54$		0			0
$55$		−	4.53076i		−	0.0823775i
$56$	−19.5717	+	2.99162i	−0.349494	+	0.0534219i
$57$		0			0
$58$	−6.05829	−	10.4933i	−0.104453	−	0.180918i
$59$	−29.8476	−	17.2325i	−0.505891	−	0.292077i	0.225252	−	0.974301i	$-0.427680\pi$
$59$	−29.8476	−	17.2325i	−0.505891	−	0.292077i	−0.731143	+	0.682224i	$0.761013\pi$
$60$		0			0
$61$	58.8187	−	33.9590i	0.964240	−	0.556704i	0.0667649	−	0.997769i	$-0.478732\pi$
$61$	58.8187	−	33.9590i	0.964240	−	0.556704i	0.897476	+	0.441064i	$0.145399\pi$
$62$			61.5860i			0.993322i
$63$		0			0
$64$	8.00000			0.125000
$65$	1.20819	+	2.09265i	0.0185875	+	0.0321946i
$66$		0			0
$67$	−36.5287	+	63.2696i	−0.545205	+	0.944323i	0.453389	+	0.891313i	$0.350215\pi$
$67$	−36.5287	+	63.2696i	−0.545205	+	0.944323i	−0.998594	+	0.0530102i	$0.983118\pi$
$68$	−34.1058	+	19.6910i	−0.501557	+	0.289574i
$69$		0			0
$70$	2.13653	+	0.833397i	0.0305218	+	0.0119057i
$71$	2.57953			0.0363314			0.0181657	−	0.999835i	$-0.494217\pi$
$71$	2.57953			0.0363314			0.0181657	+	0.999835i	$0.494217\pi$
$72$		0			0
$73$	−116.231	−	67.1059i	−1.59220	−	0.919259i	−0.992928	−	0.118716i	$-0.962122\pi$
$73$	−116.231	−	67.1059i	−1.59220	−	0.919259i	−0.599275	−	0.800543i	$-0.704544\pi$
$74$	−41.5838	+	72.0253i	−0.561943	+	0.973314i
$75$		0			0
$76$			14.9704i			0.196979i
$77$	49.7516	−	127.545i	0.646125	−	1.65643i
$78$		0			0
$79$	−47.1107	−	81.5982i	−0.596338	−	1.03289i	−0.993357	−	0.115078i	$-0.963288\pi$
$79$	−47.1107	−	81.5982i	−0.596338	−	1.03289i	0.397018	−	0.917811i	$-0.370045\pi$
$80$	−0.802493	−	0.463320i	−0.0100312	−	0.00579149i
$81$		0			0
$82$	85.2695	−	49.2304i	1.03987	−	0.600370i
$83$		−	66.7610i		−	0.804349i	−0.915563	−	0.402174i	$-0.868255\pi$
$83$		−	66.7610i		−	0.804349i	0.915563	−	0.402174i	$-0.131745\pi$
$84$		0			0
$85$	4.56162			0.0536661
$86$	−7.62837	−	13.2127i	−0.0887020	−	0.153636i
$87$		0			0
$88$	−27.6589	+	47.9067i	−0.314306	+	0.544394i
$89$	37.4365	−	21.6140i	0.420634	−	0.242853i	−0.274714	−	0.961526i	$-0.588583\pi$
$89$	37.4365	−	21.6140i	0.420634	−	0.242853i	0.695349	+	0.718673i	$0.255250\pi$
$90$		0			0
$91$	11.0326	+	72.1768i	0.121237	+	0.793152i
$92$	10.7984			0.117374
$93$		0			0
$94$	10.9861	+	6.34281i	0.116873	+	0.0674767i
$95$	0.867008	−	1.50170i	0.00912640	−	0.0158074i
$96$		0			0
$97$		−	13.8343i		−	0.142622i	−0.997454	−	0.0713108i	$-0.977282\pi$
$97$		−	13.8343i		−	0.142622i	0.997454	−	0.0713108i	$-0.0227182\pi$
$98$	50.9936	+	46.9217i	0.520343	+	0.478793i
$99$		0			0
$100$	−24.9463	−	43.2083i	−0.249463	−	0.432083i
$101$	−121.626	−	70.2205i	−1.20421	−	0.695253i	−0.242724	−	0.970095i	$-0.578041\pi$
$101$	−121.626	−	70.2205i	−1.20421	−	0.695253i	−0.961489	+	0.274843i	$0.911374\pi$
$102$		0			0
$103$	34.8153	−	20.1006i	0.338013	−	0.195152i	−0.321380	−	0.946950i	$-0.604147\pi$
$103$	34.8153	−	20.1006i	0.338013	−	0.195152i	0.659393	+	0.751798i	$0.270813\pi$
$104$		−	29.5026i		−	0.283679i
$105$		0			0
$106$	−87.1747			−0.822402
$107$	89.4993	+	155.017i	0.836442	+	1.44876i	0.892851	+	0.450353i	$0.148702\pi$
$107$	89.4993	+	155.017i	0.836442	+	1.44876i	−0.0564085	+	0.998408i	$0.517965\pi$
$108$		0			0
$109$	−27.5473	+	47.7134i	−0.252728	+	0.437738i	−0.964276	−	0.264900i	$-0.914661\pi$
$109$	−27.5473	+	47.7134i	−0.252728	+	0.437738i	0.711548	+	0.702637i	$0.247994\pi$
$110$	5.54903	−	3.20373i	0.0504457	−	0.0291248i
$111$		0			0
$112$	−17.5032	−	21.8549i	−0.156279	−	0.195133i
$113$	−61.8356			−0.547218			−0.273609	−	0.961841i	$-0.588217\pi$
$113$	−61.8356			−0.547218			−0.273609	+	0.961841i	$0.588217\pi$
$114$		0			0
$115$	−1.08321	−	0.625392i	−0.00941922	−	0.00543819i
$116$	8.56771	−	14.8397i	0.0738596	−	0.127929i
$117$		0			0
$118$		−	48.7409i		−	0.413059i
$119$	128.414	+	50.0904i	1.07911	+	0.420928i
$120$		0			0
$121$	−130.754	−	226.473i	−1.08061	−	1.87168i
$122$	83.1822	+	48.0252i	0.681821	+	0.393649i
$123$		0			0
$124$	−75.4271	+	43.5478i	−0.608283	+	0.351192i
$125$			11.5706i			0.0925645i
$126$		0			0
$127$	−118.146			−0.930283			−0.465141	−	0.885236i	$-0.653997\pi$
$127$	−118.146			−0.930283			−0.465141	+	0.885236i	$0.653997\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.70864	+	2.95945i	−0.0131434	+	0.0227650i
$131$	42.4180	−	24.4901i	0.323802	−	0.186947i	−0.329284	−	0.944231i	$-0.606807\pi$
$131$	42.4180	−	24.4901i	0.323802	−	0.186947i	0.653086	+	0.757284i	$0.273474\pi$
$132$		0			0
$133$	40.8970	−	32.7537i	0.307496	−	0.246269i
$134$	−103.319			−0.771037
$135$		0			0
$136$	−48.2330	−	27.8473i	−0.354654	−	0.204760i
$137$	34.9690	−	60.5681i	0.255248	−	0.442103i	−0.709715	−	0.704489i	$-0.751176\pi$
$137$	34.9690	−	60.5681i	0.255248	−	0.442103i	0.964963	+	0.262386i	$0.0845095\pi$
$138$		0			0
$139$		−	22.0618i		−	0.158718i	−0.996846	−	0.0793591i	$-0.974713\pi$
$139$		−	22.0618i		−	0.158718i	0.996846	−	0.0793591i	$-0.0252874\pi$
$140$	0.490053	+	3.20600i	0.00350038	+	0.0229000i
$141$		0			0
$142$	1.82400	+	3.15926i	0.0128451	+	0.0222483i
$143$	176.671	+	102.001i	1.23546	+	0.713295i
$144$		0			0
$145$	−1.71888	+	0.992397i	−0.0118544	+	0.00684412i
$146$		−	189.804i		−	1.30003i
$147$		0			0
$148$	−117.617			−0.794708
$149$	−95.0620	−	164.652i	−0.638000	−	1.10505i	−0.985871	−	0.167506i	$-0.946429\pi$
$149$	−95.0620	−	164.652i	−0.638000	−	1.10505i	0.347871	−	0.937542i	$-0.386905\pi$
$150$		0			0
$151$	43.5724	−	75.4696i	0.288559	−	0.499799i	−0.684907	−	0.728630i	$-0.740157\pi$
$151$	43.5724	−	75.4696i	0.288559	−	0.499799i	0.973466	+	0.228832i	$0.0734906\pi$
$152$	−18.3349	+	10.5856i	−0.120624	+	0.0696424i
$153$		0			0
$154$	191.390	−	29.2548i	1.24279	−	0.189967i
$155$	10.0883			0.0650857
$156$		0			0
$157$	−96.1944	−	55.5379i	−0.612703	−	0.353744i	0.161320	−	0.986902i	$-0.448425\pi$
$157$	−96.1944	−	55.5379i	−0.612703	−	0.353744i	−0.774023	+	0.633158i	$0.781758\pi$
$158$	66.6246	−	115.397i	0.421675	−	0.730362i
$159$		0			0
$160$		−	1.31047i		−	0.00819041i
$161$	−23.6260	−	29.4999i	−0.146745	−	0.183229i
$162$		0			0
$163$	−152.157	−	263.544i	−0.933481	−	1.61684i	−0.777321	−	0.629105i	$-0.783422\pi$
$163$	−152.157	−	263.544i	−0.933481	−	1.61684i	−0.156160	−	0.987732i	$-0.549912\pi$
$164$	120.589	+	69.6222i	0.735300	+	0.424526i
$165$		0			0
$166$	81.7651	−	47.2071i	0.492561	−	0.284380i
$167$			4.93753i			0.0295660i	0.999891	+	0.0147830i	$0.00470575\pi$
$167$			4.93753i			0.0295660i	−0.999891	+	0.0147830i	$0.995294\pi$
$168$		0			0
$169$	60.1998			0.356212
$170$	3.22555	+	5.58682i	0.0189738	+	0.0328636i
$171$		0			0
$172$	10.7881	−	18.6856i	0.0627218	−	0.108637i
$173$	−119.623	+	69.0646i	−0.691465	+	0.399217i	−0.804161	−	0.594412i	$-0.797385\pi$
$173$	−119.623	+	69.0646i	−0.691465	+	0.399217i	0.112696	+	0.993630i	$0.464051\pi$
$174$		0			0
$175$	−63.4590	+	162.686i	−0.362623	+	0.929632i
$176$	−78.2313			−0.444496
$177$		0			0
$178$	52.9432	+	30.5667i	0.297433	+	0.171723i
$179$	−87.6220	+	151.766i	−0.489508	+	0.847853i	−0.999927	−	0.0120726i	$-0.996157\pi$
$179$	−87.6220	+	151.766i	−0.489508	+	0.847853i	0.510419	+	0.859926i	$0.329490\pi$
$180$		0			0
$181$			324.992i			1.79553i	0.440471	+	0.897767i	$0.354812\pi$
$181$			324.992i			1.79553i	−0.440471	+	0.897767i	$0.645188\pi$
$182$	−80.5970	+	64.5488i	−0.442840	+	0.354664i
$183$		0			0
$184$	7.63566	+	13.2253i	0.0414981	+	0.0718769i
$185$	11.7983	+	6.81177i	0.0637748	+	0.0368204i
$186$		0			0
$187$	333.518	−	192.557i	1.78352	−	1.02972i
$188$			17.9402i			0.0954265i
$189$		0			0
$190$	2.45227			0.0129067
$191$	133.192	+	230.696i	0.697341	+	1.20783i	0.969385	+	0.245545i	$0.0789670\pi$
$191$	133.192	+	230.696i	0.697341	+	1.20783i	−0.272044	+	0.962285i	$0.587700\pi$
$192$		0			0
$193$	−152.383	+	263.935i	−0.789549	+	1.36754i	0.136695	+	0.990613i	$0.456352\pi$
$193$	−152.383	+	263.935i	−0.789549	+	1.36754i	−0.926244	+	0.376926i	$0.876981\pi$
$194$	16.9435	−	9.78232i	0.0873375	−	0.0504243i
$195$		0			0
$196$	−21.4092	+	95.6329i	−0.109231	+	0.487923i
$197$	−209.399			−1.06294			−0.531471	−	0.847077i	$-0.678360\pi$
$197$	−209.399			−1.06294			−0.531471	+	0.847077i	$0.678360\pi$
$198$		0			0
$199$	105.797	+	61.0818i	0.531642	+	0.306944i	0.741685	−	0.670748i	$-0.234027\pi$
$199$	105.797	+	61.0818i	0.531642	+	0.306944i	−0.210043	+	0.977692i	$0.567360\pi$
$200$	35.2794	−	61.1058i	0.176397	−	0.305529i
$201$		0			0
$202$		−	198.614i		−	0.983236i
$203$	−59.2854	+	9.06206i	−0.292046	+	0.0446407i
$204$		0			0
$205$	−8.06434	−	13.9678i	−0.0393382	−	0.0681358i
$206$	49.2363	+	28.4266i	0.239011	+	0.137993i
$207$		0			0
$208$	36.1331	−	20.8615i	0.173717	−	0.100296i
$209$		−	146.394i		−	0.700450i
$210$		0			0
$211$	−225.780			−1.07005			−0.535023	−	0.844838i	$-0.679697\pi$
$211$	−225.780			−1.07005			−0.535023	+	0.844838i	$0.679697\pi$
$212$	−61.6418	−	106.767i	−0.290763	−	0.503617i
$213$		0			0
$214$	−126.571	+	219.228i	−0.591454	+	1.02443i
$215$	−2.16435	+	1.24959i	−0.0100668	+	0.00581204i
$216$		0			0
$217$	283.994	+	110.778i	1.30873	+	0.510497i
$218$	−77.9157			−0.357411
$219$		0			0
$220$	7.84751	+	4.53076i	0.0356705	+	0.0205944i
$221$	−102.696	+	177.874i	−0.464687	+	0.804862i
$222$		0			0
$223$			27.9689i			0.125421i	0.998032	+	0.0627105i	$0.0199745\pi$
$223$			27.9689i			0.125421i	−0.998032	+	0.0627105i	$0.980026\pi$
$224$	14.3900	−	36.8907i	0.0642412	−	0.164691i
$225$		0			0
$226$	−43.7244	−	75.7329i	−0.193471	−	0.335101i
$227$	−157.719	−	91.0593i	−0.694799	−	0.401142i	0.110609	−	0.993864i	$-0.464720\pi$
$227$	−157.719	−	91.0593i	−0.694799	−	0.401142i	−0.805407	+	0.592722i	$0.798053\pi$
$228$		0			0
$229$	325.016	−	187.648i	1.41928	−	0.819423i	0.423047	−	0.906108i	$-0.360960\pi$
$229$	325.016	−	187.648i	1.41928	−	0.819423i	0.996236	+	0.0866842i	$0.0276271\pi$
$230$		−	1.76887i		−	0.00769076i
$231$		0			0
$232$	24.2331			0.104453
$233$	−8.75752	−	15.1685i	−0.0375859	−	0.0651007i	0.846621	−	0.532197i	$-0.178633\pi$
$233$	−8.75752	−	15.1685i	−0.0375859	−	0.0651007i	−0.884206	+	0.467096i	$0.845300\pi$
$234$		0			0
$235$	1.03900	−	1.79961i	0.00442129	−	0.00765791i
$236$	59.6952	−	34.4650i	0.252946	−	0.146038i
$237$		0			0
$238$	29.4541	+	192.693i	0.123757	+	0.809635i
$239$	249.150			1.04247			0.521235	−	0.853413i	$-0.325472\pi$
$239$	249.150			1.04247			0.521235	+	0.853413i	$0.325472\pi$
$240$		0			0
$241$	54.0420	+	31.2012i	0.224241	+	0.129465i	0.607912	−	0.794004i	$-0.292007\pi$
$241$	54.0420	+	31.2012i	0.224241	+	0.129465i	−0.383672	+	0.923470i	$0.625341\pi$
$242$	184.915	−	320.281i	0.764110	−	1.32348i
$243$		0			0
$244$			135.836i			0.556704i
$245$	7.68616	−	8.35318i	0.0313721	−	0.0340946i
$246$		0			0
$247$	39.0380	+	67.6158i	0.158048	+	0.273748i
$248$	−106.670	−	61.5860i	−0.430121	−	0.248330i
$249$		0			0
$250$	−14.1710	+	8.18162i	−0.0566839	+	0.0327265i
$251$			286.473i			1.14133i	0.821184	+	0.570663i	$0.193314\pi$
$251$			286.473i			1.14133i	−0.821184	+	0.570663i	$0.806686\pi$
$252$		0			0
$253$	−105.597			−0.417380
$254$	−83.5418	−	144.699i	−0.328905	−	0.569680i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−238.664	+	137.793i	−0.928653	+	0.536158i	−0.886385	−	0.462948i	$-0.846791\pi$
$257$	−238.664	+	137.793i	−0.928653	+	0.536158i	−0.0422674	+	0.999106i	$0.513458\pi$
$258$		0			0
$259$	257.334	+	321.313i	0.993569	+	1.24059i
$260$	−4.83276			−0.0185875
$261$		0			0
$262$	59.9882	+	34.6342i	0.228962	+	0.132192i
$263$	−237.936	+	412.117i	−0.904699	+	1.56698i	−0.0833773	+	0.996518i	$0.526571\pi$
$263$	−237.936	+	412.117i	−0.904699	+	1.56698i	−0.821321	+	0.570466i	$0.806763\pi$
$264$		0			0
$265$			14.2799i			0.0538865i
$266$	69.0335	+	26.9280i	0.259524	+	0.101233i
$267$		0			0
$268$	−73.0575	−	126.539i	−0.272603	−	0.472162i
$269$	−381.253	−	220.116i	−1.41730	−	0.818276i	−0.421236	−	0.906951i	$-0.638403\pi$
$269$	−381.253	−	220.116i	−1.41730	−	0.818276i	−0.996061	+	0.0886750i	$0.971737\pi$
$270$		0			0
$271$	−138.802	+	80.1373i	−0.512184	+	0.295710i	−0.733731	−	0.679440i	$-0.762223\pi$
$271$	−138.802	+	80.1373i	−0.512184	+	0.295710i	0.221547	+	0.975150i	$0.428889\pi$
$272$		−	78.7641i		−	0.289574i
$273$		0			0
$274$	98.9072			0.360975
$275$	243.948	+	422.530i	0.887084	+	1.53647i
$276$		0			0
$277$	−67.6401	+	117.156i	−0.244188	+	0.422946i	−0.961903	−	0.273391i	$-0.911855\pi$
$277$	−67.6401	+	117.156i	−0.244188	+	0.422946i	0.717715	+	0.696337i	$0.245188\pi$
$278$	27.0201	−	15.6001i	0.0971947	−	0.0561154i
$279$		0			0
$280$	−3.58001	+	2.86717i	−0.0127858	+	0.0102399i
$281$	359.221			1.27837			0.639183	−	0.769054i	$-0.279273\pi$
$281$	359.221			1.27837			0.639183	+	0.769054i	$0.279273\pi$
$282$		0			0
$283$	338.295	+	195.315i	1.19539	+	0.690158i	0.959524	−	0.281628i	$-0.0908745\pi$
$283$	338.295	+	195.315i	1.19539	+	0.690158i	0.235865	+	0.971786i	$0.424208\pi$
$284$	−2.57953	+	4.46787i	−0.00908284	+	0.0157319i
$285$		0			0
$286$			288.503i			1.00875i
$287$	−73.6394	−	481.760i	−0.256583	−	1.67861i
$288$		0			0
$289$	49.3681	+	85.5081i	0.170824	+	0.295876i
$290$	−2.43087	−	1.40346i	−0.00838230	−	0.00483952i
$291$		0			0
$292$	232.462	−	134.212i	0.796102	−	0.459630i
$293$			365.315i			1.24681i	0.781899	+	0.623405i	$0.214251\pi$
$293$			365.315i			1.24681i	−0.781899	+	0.623405i	$0.785749\pi$
$294$		0			0
$295$	−7.98416			−0.0270650
$296$	−83.1676	−	144.051i	−0.280972	−	0.486657i
$297$		0			0
$298$	134.438	−	232.853i	0.451134	−	0.781387i
$299$	48.7727	−	28.1589i	0.163119	−	0.0941770i
$300$		0			0
$301$	−74.6500	+	11.4106i	−0.248007	+	0.0379090i
$302$	123.241			0.408084
$303$		0			0
$304$	−25.9294	−	14.9704i	−0.0852942	−	0.0492446i
$305$	7.86693	−	13.6259i	0.0257932	−	0.0446751i
$306$		0			0
$307$			221.404i			0.721185i	0.932723	+	0.360592i	$0.117425\pi$
$307$			221.404i			0.721185i	−0.932723	+	0.360592i	$0.882575\pi$
$308$	171.163	+	213.717i	0.555723	+	0.693887i
$309$		0			0
$310$	7.13349	+	12.3556i	0.0230113	+	0.0398567i
$311$	96.9709	+	55.9862i	0.311803	+	0.180020i	0.647733	−	0.761867i	$-0.275717\pi$
$311$	96.9709	+	55.9862i	0.311803	+	0.180020i	−0.335930	+	0.941887i	$0.609050\pi$
$312$		0			0
$313$	241.946	−	139.688i	0.772991	−	0.446286i	−0.0609497	−	0.998141i	$-0.519413\pi$
$313$	241.946	−	139.688i	0.772991	−	0.446286i	0.833940	+	0.551854i	$0.186080\pi$
$314$		−	157.085i		−	0.500270i
$315$		0			0
$316$	188.443			0.596338
$317$	−57.2433	−	99.1483i	−0.180578	−	0.312771i	0.761499	−	0.648166i	$-0.224464\pi$
$317$	−57.2433	−	99.1483i	−0.180578	−	0.312771i	−0.942078	+	0.335395i	$0.891130\pi$
$318$		0			0
$319$	−83.7829	+	145.116i	−0.262642	+	0.454910i
$320$	1.60499	−	0.926639i	0.00501558	−	0.00289575i
$321$		0			0
$322$	19.4237	−	49.7954i	0.0603222	−	0.154644i
$323$	147.391			0.456319
$324$		0			0
$325$	−225.347	−	130.104i	−0.693376	−	0.400321i
$326$	215.183	−	372.708i	0.660071	−	1.14328i
$327$		0			0
$328$			196.921i			0.600370i
$329$	49.0101	−	39.2514i	0.148967	−	0.119305i
$330$		0			0
$331$	−118.777	−	205.728i	−0.358844	−	0.621535i	0.628924	−	0.777467i	$-0.283496\pi$
$331$	−118.777	−	205.728i	−0.358844	−	0.621535i	−0.987768	+	0.155931i	$0.950162\pi$
$332$	115.633	+	66.7610i	0.348293	+	0.201087i
$333$		0			0
$334$	−6.04721	+	3.49136i	−0.0181054	+	0.0104532i
$335$			16.9245i			0.0505208i
$336$		0			0
$337$	144.487			0.428746			0.214373	−	0.976752i	$-0.431229\pi$
$337$	144.487			0.428746			0.214373	+	0.976752i	$0.431229\pi$
$338$	42.5677	+	73.7294i	0.125940	+	0.218134i
$339$		0			0
$340$	−4.56162	+	7.90095i	−0.0134165	+	0.0232381i
$341$	737.595	−	425.851i	2.16304	−	1.24883i
$342$		0			0
$343$	308.097	−	150.749i	0.898242	−	0.439500i
$344$	30.5135			0.0887020
$345$		0			0
$346$	−169.173	−	97.6721i	−0.488939	−	0.282289i
$347$	−15.4396	+	26.7422i	−0.0444945	+	0.0770667i	−0.887415	−	0.460971i	$-0.847501\pi$
$347$	−15.4396	+	26.7422i	−0.0444945	+	0.0770667i	0.842920	+	0.538038i	$0.180834\pi$
$348$		0			0
$349$		−	520.033i		−	1.49007i	−0.667027	−	0.745034i	$-0.732433\pi$
$349$		−	520.033i		−	1.49007i	0.667027	−	0.745034i	$-0.267567\pi$
$350$	−244.121	+	37.3150i	−0.697488	+	0.106614i
$351$		0			0
$352$	−55.3179	−	95.8134i	−0.157153	−	0.272197i
$353$	−251.467	−	145.185i	−0.712373	−	0.411288i	0.0995664	−	0.995031i	$-0.468254\pi$
$353$	−251.467	−	145.185i	−0.712373	−	0.411288i	−0.811939	+	0.583742i	$0.801588\pi$
$354$		0			0
$355$	0.517513	−	0.298786i	0.00145778	−	0.000841652i
$356$			86.4558i			0.242853i
$357$		0			0
$358$	−247.832			−0.692269
$359$	−131.971	−	228.580i	−0.367606	−	0.636713i	0.621585	−	0.783347i	$-0.286489\pi$
$359$	−131.971	−	228.580i	−0.367606	−	0.636713i	−0.989191	+	0.146635i	$0.953156\pi$
$360$		0			0
$361$	−152.486	+	264.114i	−0.422399	+	0.731616i
$362$	−398.032	+	229.804i	−1.09954	+	0.634817i
$363$		0			0
$364$	−136.046	−	53.0678i	−0.373754	−	0.145791i
$365$	−31.0915			−0.0851821
$366$		0			0
$367$	−218.412	−	126.100i	−0.595127	−	0.343597i	0.171995	−	0.985098i	$-0.444979\pi$
$367$	−218.412	−	126.100i	−0.595127	−	0.343597i	−0.767122	+	0.641501i	$0.778312\pi$
$368$	−10.7984	+	18.7035i	−0.0293436	+	0.0508246i
$369$		0			0
$370$			19.2666i			0.0520719i
$371$	−156.806	+	401.992i	−0.422657	+	1.08354i
$372$		0			0
$373$	−215.182	−	372.706i	−0.576895	−	0.999211i	−0.995833	−	0.0911966i	$-0.970931\pi$
$373$	−215.182	−	372.706i	−0.576895	−	0.999211i	0.418938	−	0.908015i	$-0.362402\pi$
$374$	471.666	+	272.316i	1.26114	+	0.728119i
$375$		0			0
$376$	−21.9721	+	12.6856i	−0.0584365	+	0.0337384i
$377$		−	89.3675i		−	0.237049i
$378$		0			0
$379$	−308.710			−0.814537			−0.407269	−	0.913308i	$-0.633519\pi$
$379$	−308.710			−0.814537			−0.407269	+	0.913308i	$0.633519\pi$
$380$	1.73402	+	3.00340i	0.00456320	+	0.00790369i
$381$		0			0
$382$	−188.362	+	326.253i	−0.493095	+	0.854065i
$383$	203.418	−	117.443i	0.531118	−	0.306641i	−0.210354	−	0.977625i	$-0.567462\pi$
$383$	203.418	−	117.443i	0.531118	−	0.306641i	0.741471	+	0.670984i	$0.234128\pi$
$384$		0			0
$385$	−4.79218	−	31.3512i	−0.0124472	−	0.0814317i
$386$	−431.004			−1.11659
$387$		0			0
$388$	23.9617	+	13.8343i	0.0617570	+	0.0356554i
$389$	−166.673	+	288.686i	−0.428466	+	0.742124i	−0.996737	−	0.0807170i	$-0.974279\pi$
$389$	−166.673	+	288.686i	−0.428466	+	0.742124i	0.568272	+	0.822841i	$0.307612\pi$
$390$		0			0
$391$		−	106.316i		−	0.271909i
$392$	−132.264	+	41.4019i	−0.337409	+	0.105617i
$393$		0			0
$394$	−148.068	−	256.461i	−0.375807	−	0.650916i
$395$	−18.9030	−	10.9137i	−0.0478557	−	0.0276295i
$396$		0			0
$397$	176.636	−	101.981i	0.444927	−	0.256879i	−0.260758	−	0.965404i	$-0.583973\pi$
$397$	176.636	−	101.981i	0.444927	−	0.256879i	0.705685	+	0.708525i	$0.250639\pi$
$398$			172.765i			0.434084i
$399$		0			0
$400$	99.7853			0.249463
$401$	−194.022	−	336.056i	−0.483846	−	0.838045i	0.515982	−	0.856599i	$-0.327427\pi$
$401$	−194.022	−	336.056i	−0.483846	−	0.838045i	−0.999828	+	0.0185542i	$0.994094\pi$
$402$		0			0
$403$	−227.118	+	393.380i	−0.563568	+	0.976129i
$404$	243.251	−	140.441i	0.602107	−	0.347626i
$405$		0			0
$406$	−53.0198	−	66.2016i	−0.130591	−	0.163058i
$407$	1150.16			2.82596
$408$		0			0
$409$	308.783	+	178.276i	0.754970	+	0.435882i	0.827487	−	0.561485i	$-0.189770\pi$
$409$	308.783	+	178.276i	0.754970	+	0.435882i	−0.0725168	+	0.997367i	$0.523103\pi$
$410$	11.4047	−	19.7535i	0.0278163	−	0.0481793i
$411$		0			0
$412$			80.4025i			0.195152i
$413$	−224.761	−	87.6729i	−0.544216	−	0.212283i
$414$		0			0
$415$	−7.73291	−	13.3938i	−0.0186335	−	0.0322742i
$416$	51.0999	+	29.5026i	0.122836	+	0.0709196i
$417$		0			0
$418$	179.295	−	103.516i	0.428936	−	0.247646i
$419$			508.608i			1.21386i	0.794755	+	0.606931i	$0.207600\pi$
$419$			508.608i			1.21386i	−0.794755	+	0.606931i	$0.792400\pi$
$420$		0			0
$421$	−442.316			−1.05063			−0.525316	−	0.850907i	$-0.676053\pi$
$421$	−442.316			−1.05063			−0.525316	+	0.850907i	$0.676053\pi$
$422$	−159.650	−	276.522i	−0.378318	−	0.655266i
$423$		0			0
$424$	87.1747	−	150.991i	0.205601	−	0.356111i
$425$	−425.408	+	245.609i	−1.00096	+	0.577904i
$426$		0			0
$427$	371.085	−	297.196i	0.869051	−	0.696009i
$428$	−357.997			−0.836442
$429$		0			0
$430$	−3.06086	−	1.76719i	−0.00711827	−	0.00410974i
$431$	417.826	−	723.697i	0.969435	−	1.67911i	0.272239	−	0.962230i	$-0.412236\pi$
$431$	417.826	−	723.697i	0.969435	−	1.67911i	0.697196	−	0.716881i	$-0.254431\pi$
$432$		0			0
$433$			44.2041i			0.102088i	0.998696	+	0.0510440i	$0.0162549\pi$
$433$			44.2041i			0.102088i	−0.998696	+	0.0510440i	$0.983745\pi$
$434$	65.1394	+	426.152i	0.150091	+	0.981917i
$435$		0			0
$436$	−55.0947	−	95.4268i	−0.126364	−	0.218869i
$437$	−34.9997	−	20.2071i	−0.0800909	−	0.0462405i
$438$		0			0
$439$	−130.991	+	75.6277i	−0.298385	+	0.172273i	−0.641717	−	0.766941i	$-0.721778\pi$
$439$	−130.991	+	75.6277i	−0.298385	+	0.172273i	0.343332	+	0.939214i	$0.388444\pi$
$440$			12.8149i			0.0291248i
$441$		0			0
$442$	−290.468			−0.657167
$443$	−218.360	−	378.211i	−0.492912	−	0.853749i	0.507054	−	0.861914i	$-0.330734\pi$
$443$	−218.360	−	378.211i	−0.492912	−	0.853749i	−0.999967	+	0.00816486i	$0.997401\pi$
$444$		0			0
$445$	5.00708	−	8.67252i	0.0112519	−	0.0194888i
$446$	−34.2547	+	19.7770i	−0.0768043	+	0.0443430i
$447$		0			0
$448$	55.3570	−	8.46159i	0.123565	−	0.0188875i
$449$	−524.276			−1.16765			−0.583827	−	0.811878i	$-0.698445\pi$
$449$	−524.276			−1.16765			−0.583827	+	0.811878i	$0.698445\pi$
$450$		0			0
$451$	−1179.23	−	680.830i	−2.61471	−	1.50960i
$452$	61.8356	−	107.102i	0.136804	−	0.236952i
$453$		0			0
$454$		−	257.555i		−	0.567301i
$455$	10.5736	+	13.2024i	0.0232387	+	0.0290164i
$456$		0			0
$457$	−99.5556	−	172.435i	−0.217846	−	0.377320i	0.736303	−	0.676652i	$-0.236570\pi$
$457$	−99.5556	−	172.435i	−0.217846	−	0.377320i	−0.954149	+	0.299332i	$0.903236\pi$
$458$	459.642	+	265.374i	1.00358	+	0.579420i
$459$		0			0
$460$	2.16642	−	1.25078i	0.00470961	−	0.00271909i
$461$		−	676.203i		−	1.46682i	−0.679788	−	0.733408i	$-0.737928\pi$
$461$		−	676.203i		−	1.46682i	0.679788	−	0.733408i	$-0.262072\pi$
$462$		0			0
$463$	334.085			0.721566			0.360783	−	0.932650i	$-0.382509\pi$
$463$	334.085			0.721566			0.360783	+	0.932650i	$0.382509\pi$
$464$	17.1354	+	29.6794i	0.0369298	+	0.0639643i
$465$		0			0
$466$	12.3850	−	21.4514i	0.0265772	−	0.0460331i
$467$	−564.271	+	325.782i	−1.20829	+	0.697606i	−0.962385	−	0.271688i	$-0.912418\pi$
$467$	−564.271	+	325.782i	−1.20829	+	0.697606i	−0.245904	+	0.969294i	$0.579085\pi$
$468$		0			0
$469$	−185.845	+	476.439i	−0.396258	+	1.01586i
$470$	2.93875			0.00625266
$471$		0			0
$472$	84.4217	+	48.7409i	0.178860	+	0.103265i
$473$	−105.496	+	182.725i	−0.223037	+	0.386311i
$474$		0			0
$475$			186.728i			0.393111i
$476$	−215.173	+	172.328i	−0.452043	+	0.362034i
$477$		0			0
$478$	176.176	+	305.146i	0.368569	+	0.638380i
$479$	−129.703	−	74.8843i	−0.270780	−	0.156335i	0.358462	−	0.933544i	$-0.383301\pi$
$479$	−129.703	−	74.8843i	−0.270780	−	0.156335i	−0.629242	+	0.777210i	$0.716635\pi$
$480$		0			0
$481$	−531.233	+	306.707i	−1.10443	+	0.637645i
$482$			88.2502i			0.183092i
$483$		0			0
$484$	523.017			1.08061
$485$	−1.60242	−	2.77548i	−0.00330397	−	0.00572264i
$486$		0			0
$487$	450.535	−	780.350i	0.925123	−	1.60236i	0.133761	−	0.991014i	$-0.457295\pi$
$487$	450.535	−	780.350i	0.925123	−	1.60236i	0.791363	−	0.611347i	$-0.209372\pi$
$488$	−166.364	+	96.0505i	−0.340910	+	0.196825i
$489$		0			0
$490$	15.6654	+	3.50700i	0.0319703	+	0.00715714i
$491$	−252.264			−0.513775			−0.256888	−	0.966441i	$-0.582697\pi$
$491$	−252.264			−0.513775			−0.256888	+	0.966441i	$0.582697\pi$
$492$		0			0
$493$	−146.105	−	84.3535i	−0.296358	−	0.171102i
$494$	−55.2080	+	95.6231i	−0.111757	+	0.193569i
$495$		0			0
$496$		−	174.191i		−	0.351192i
$497$	17.8494	−	2.72836i	0.0359142	−	0.00548967i
$498$		0			0
$499$	−145.343	−	251.741i	−0.291268	−	0.504491i	0.682842	−	0.730566i	$-0.260744\pi$
$499$	−145.343	−	251.741i	−0.291268	−	0.504491i	−0.974110	+	0.226075i	$0.927411\pi$
$500$	−20.0408	−	11.5706i	−0.0400816	−	0.0231411i
$501$		0			0
$502$	−350.856	+	202.567i	−0.698917	+	0.403520i
$503$			818.534i			1.62730i	0.581353	+	0.813652i	$0.302524\pi$
$503$			818.534i			1.62730i	−0.581353	+	0.813652i	$0.697476\pi$
$504$		0			0
$505$	−32.5345			−0.0644248
$506$	−74.6684	−	129.330i	−0.147566	−	0.255592i
$507$		0			0
$508$	118.146	−	204.635i	0.232571	−	0.402824i
$509$	626.081	−	361.468i	1.23002	−	0.710154i	0.262988	−	0.964799i	$-0.415292\pi$
$509$	626.081	−	361.468i	1.23002	−	0.710154i	0.967034	+	0.254646i	$0.0819588\pi$
$510$		0			0
$511$	−875.252	−	341.411i	−1.71282	−	0.668123i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−337.521	−	194.868i	−0.656657	−	0.379121i
$515$	4.65651	−	8.06531i	0.00904177	−	0.0156608i
$516$		0			0
$517$		−	175.435i		−	0.339334i
$518$	−211.563	+	542.371i	−0.408424	+	1.04705i
$519$		0			0
$520$	−3.41728	−	5.91890i	−0.00657169	−	0.0113825i
$521$	−739.428	−	426.909i	−1.41925	−	0.819402i	−0.423014	−	0.906123i	$-0.639028\pi$
$521$	−739.428	−	426.909i	−1.41925	−	0.819402i	−0.996233	+	0.0867207i	$0.972361\pi$
$522$		0			0
$523$	821.280	−	474.166i	1.57033	−	0.906628i	0.574197	−	0.818717i	$-0.305315\pi$
$523$	821.280	−	474.166i	1.57033	−	0.906628i	0.996128	−	0.0879101i	$-0.0280188\pi$
$524$			97.9603i			0.186947i
$525$		0			0
$526$	−672.984			−1.27944
$527$	428.751	+	742.618i	0.813569	+	1.40914i
$528$		0			0
$529$	249.924	−	432.881i	0.472446	−	0.818301i
$530$	−17.4893	+	10.0974i	−0.0329986	+	0.0190518i
$531$		0			0
$532$	15.8341	+	103.589i	0.0297634	+	0.194717i
$533$	726.211			1.36250
$534$		0			0
$535$	35.9113	+	20.7334i	0.0671239	+	0.0387540i
$536$	103.319	−	178.954i	0.192759	−	0.333869i
$537$		0			0
$538$		−	622.583i		−	1.15722i
$539$	209.359	−	935.186i	0.388420	−	1.73504i
$540$		0			0
$541$	229.321	+	397.195i	0.423883	+	0.734187i	0.996315	−	0.0857650i	$-0.0273334\pi$
$541$	229.321	+	397.195i	0.423883	+	0.734187i	−0.572432	+	0.819952i	$0.694000\pi$
$542$	−196.295	−	113.331i	−0.362169	−	0.209098i
$543$		0			0
$544$	96.4659	−	55.6946i	0.177327	−	0.102380i
$545$			12.7632i			0.0234188i
$546$		0			0
$547$	595.187			1.08809			0.544047	−	0.839055i	$-0.316891\pi$
$547$	595.187			1.08809			0.544047	+	0.839055i	$0.316891\pi$
$548$	69.9380	+	121.136i	0.127624	+	0.221051i
$549$		0			0
$550$	−344.995	+	597.548i	−0.627263	+	1.08645i
$551$	−55.5390	+	32.0654i	−0.100797	+	0.0581950i
$552$		0			0
$553$	−412.295	−	514.800i	−0.745561	−	0.930923i
$554$	−191.315			−0.345334
$555$		0			0
$556$	38.2122	+	22.0618i	0.0687270	+	0.0396796i
$557$	69.8088	−	120.912i	0.125330	−	0.217078i	−0.796532	−	0.604597i	$-0.793334\pi$
$557$	69.8088	−	120.912i	0.125330	−	0.217078i	0.921862	+	0.387519i	$0.126668\pi$
$558$		0			0
$559$		−	112.528i		−	0.201303i
$560$	−6.04301	−	2.35720i	−0.0107911	−	0.00420929i
$561$		0			0
$562$	254.008	+	439.954i	0.451971	+	0.782836i
$563$	−738.603	−	426.433i	−1.31191	−	0.757430i	−0.329495	−	0.944157i	$-0.606878\pi$
$563$	−738.603	−	426.433i	−1.31191	−	0.757430i	−0.982412	+	0.186728i	$0.940212\pi$
$564$		0			0
$565$	−12.4057	+	7.16241i	−0.0219569	+	0.0126768i
$566$			552.433i			0.976030i
$567$		0			0
$568$	−7.29601			−0.0128451
$569$	−149.339	−	258.663i	−0.262459	−	0.454592i	0.704436	−	0.709768i	$-0.251200\pi$
$569$	−149.339	−	258.663i	−0.262459	−	0.454592i	−0.966895	+	0.255176i	$0.917867\pi$
$570$		0			0
$571$	−486.893	+	843.323i	−0.852702	+	1.47692i	0.0260595	+	0.999660i	$0.491704\pi$
$571$	−486.893	+	843.323i	−0.852702	+	1.47692i	−0.878761	+	0.477262i	$0.841629\pi$
$572$	−353.343	+	204.002i	−0.617732	+	0.356648i
$573$		0			0
$574$	537.962	−	430.845i	0.937217	−	0.750601i
$575$	134.691			0.234245
$576$		0			0
$577$	782.916	+	452.017i	1.35687	+	0.783392i	0.989201	−	0.146564i	$-0.0468213\pi$
$577$	782.916	+	452.017i	1.35687	+	0.783392i	0.367673	+	0.929955i	$0.380155\pi$
$578$	−69.8171	+	120.927i	−0.120791	+	0.209216i
$579$		0			0
$580$		−	3.96959i		−	0.00684412i
$581$	−70.6130	−	461.961i	−0.121537	−	0.795114i
$582$		0			0
$583$	602.790	+	1044.06i	1.03394	+	1.79085i
$584$	328.750	+	189.804i	0.562929	+	0.325007i
$585$		0			0
$586$	−447.418	+	258.317i	−0.763512	+	0.440814i
$587$		−	670.235i		−	1.14180i	−0.821021	−	0.570899i	$-0.806595\pi$
$587$		−	670.235i		−	1.14180i	0.821021	−	0.570899i	$-0.193405\pi$
$588$		0			0
$589$	325.964			0.553419
$590$	−5.64566	−	9.77856i	−0.00956891	−	0.0165738i
$591$		0			0
$592$	117.617	−	203.718i	0.198677	−	0.344119i
$593$	964.156	−	556.655i	1.62589	−	0.938711i	0.640594	−	0.767879i	$-0.278688\pi$
$593$	964.156	−	556.655i	1.62589	−	0.938711i	0.985300	−	0.170831i	$-0.0546453\pi$
$594$		0			0
$595$	31.5647	−	4.82482i	0.0530499	−	0.00810894i
$596$	380.248			0.638000
$597$		0			0
$598$	68.9750	+	39.8227i	0.115343	+	0.0665932i
$599$	28.4445	−	49.2674i	0.0474867	−	0.0822494i	−0.841305	−	0.540561i	$-0.818212\pi$
$599$	28.4445	−	49.2674i	0.0474867	−	0.0822494i	0.888792	+	0.458311i	$0.151545\pi$
$600$		0			0
$601$			715.757i			1.19094i	0.803377	+	0.595471i	$0.203035\pi$
$601$			715.757i			1.19094i	−0.803377	+	0.595471i	$0.796965\pi$
$602$	−66.7606	−	83.3586i	−0.110898	−	0.138470i
$603$		0			0
$604$	87.1448	+	150.939i	0.144279	+	0.249899i
$605$	−52.4647	−	30.2905i	−0.0867186	−	0.0500670i
$606$		0			0
$607$	−358.401	+	206.923i	−0.590446	+	0.340894i	−0.765274	−	0.643705i	$-0.777396\pi$
$607$	−358.401	+	206.923i	−0.590446	+	0.340894i	0.174828	+	0.984599i	$0.444063\pi$
$608$		−	42.3426i		−	0.0696424i
$609$		0			0
$610$	22.2510			0.0364771
$611$	46.7823	+	81.0293i	0.0765668	+	0.132618i
$612$		0			0
$613$	188.334	−	326.204i	0.307233	−	0.532144i	−0.670523	−	0.741889i	$-0.733930\pi$
$613$	188.334	−	326.204i	0.307233	−	0.532144i	0.977756	+	0.209745i	$0.0672634\pi$
$614$	−271.163	+	156.556i	−0.441634	+	0.254977i
$615$		0			0
$616$	−140.719	+	360.751i	−0.228440	+	0.585636i
$617$	1087.06			1.76185			0.880925	−	0.473256i	$-0.156922\pi$
$617$	1087.06			1.76185			0.880925	+	0.473256i	$0.156922\pi$
$618$		0			0
$619$	247.812	+	143.074i	0.400342	+	0.231138i	0.686632	−	0.727006i	$-0.259089\pi$
$619$	247.812	+	143.074i	0.400342	+	0.231138i	−0.286290	+	0.958143i	$0.592422\pi$
$620$	−10.0883	+	17.4734i	−0.0162714	+	0.0281829i
$621$		0			0
$622$			158.353i			0.254586i
$623$	236.185	−	189.157i	0.379110	−	0.303623i
$624$		0			0
$625$	−310.489	−	537.783i	−0.496782	−	0.860452i
$626$	342.163	+	197.548i	0.546587	+	0.315572i
$627$		0			0
$628$	192.389	−	111.076i	0.306352	−	0.176872i
$629$			1158.00i			1.84101i
$630$		0			0
$631$	469.754			0.744460			0.372230	−	0.928140i	$-0.378593\pi$
$631$	469.754			0.744460			0.372230	+	0.928140i	$0.378593\pi$
$632$	133.249	+	230.795i	0.210837	+	0.365181i
$633$		0			0
$634$	80.9543	−	140.217i	0.127688	−	0.221162i
$635$	−23.7028	+	13.6848i	−0.0373273	+	0.0215509i
$636$		0			0
$637$	152.683	+	487.768i	0.239690	+	0.765726i
$638$	−236.974			−0.371432
$639$		0			0
$640$	2.26979	+	1.31047i	0.00354655	+	0.00204760i
$641$	−492.080	+	852.307i	−0.767675	+	1.32965i	0.171146	+	0.985246i	$0.445253\pi$
$641$	−492.080	+	852.307i	−0.767675	+	1.32965i	−0.938821	+	0.344406i	$0.888080\pi$
$642$		0			0
$643$			790.564i			1.22949i	0.788725	+	0.614747i	$0.210742\pi$
$643$			790.564i			1.22949i	−0.788725	+	0.614747i	$0.789258\pi$
$644$	74.7213	−	11.4215i	0.116027	−	0.0177353i
$645$		0			0
$646$	104.221	+	180.516i	0.161333	+	0.279437i
$647$	838.514	+	484.116i	1.29600	+	0.748247i	0.979711	−	0.200415i	$-0.0642290\pi$
$647$	838.514	+	484.116i	1.29600	+	0.748247i	0.316291	+	0.948662i	$0.397562\pi$
$648$		0			0
$649$	−583.754	+	337.031i	−0.899467	+	0.519308i
$650$		−	367.990i		−	0.566139i
$651$		0			0
$652$	608.630			0.933481
$653$	−109.610	−	189.851i	−0.167857	−	0.290736i	0.769809	−	0.638274i	$-0.220351\pi$
$653$	−109.610	−	189.851i	−0.167857	−	0.290736i	−0.937666	+	0.347538i	$0.887018\pi$
$654$		0			0
$655$	5.67336	−	9.82655i	0.00866162	−	0.0150024i
$656$	−241.178	+	139.244i	−0.367650	+	0.212263i
$657$		0			0
$658$	82.7283	+	32.2699i	0.125727	+	0.0490425i
$659$	192.233			0.291703			0.145852	−	0.989306i	$-0.453408\pi$
$659$	192.233			0.291703			0.145852	+	0.989306i	$0.453408\pi$
$660$		0			0
$661$	379.670	+	219.203i	0.574387	+	0.331623i	0.758900	−	0.651207i	$-0.225737\pi$
$661$	379.670	+	219.203i	0.574387	+	0.331623i	−0.184512	+	0.982830i	$0.559071\pi$
$662$	167.976	−	290.944i	0.253741	−	0.439492i
$663$		0			0
$664$			188.829i			0.284380i
$665$	4.41103	−	11.3083i	0.00663312	−	0.0170049i
$666$		0			0
$667$	23.1295	+	40.0615i	0.0346769	+	0.0600622i
$668$	−8.55205	−	4.93753i	−0.0128025	−	0.00739151i
$669$		0			0
$670$	−20.7282	+	11.9674i	−0.0309376	+	0.0178618i
$671$		−	1328.33i		−	1.97962i
$672$		0			0
$673$	−447.196			−0.664481			−0.332241	−	0.943195i	$-0.607805\pi$
$673$	−447.196			−0.664481			−0.332241	+	0.943195i	$0.607805\pi$
$674$	102.168	+	176.960i	0.151585	+	0.262552i
$675$		0			0
$676$	−60.1998	+	104.269i	−0.0890530	+	0.154244i
$677$	−96.3332	+	55.6180i	−0.142294	+	0.0821536i	−0.569457	−	0.822021i	$-0.692846\pi$
$677$	−96.3332	+	55.6180i	−0.142294	+	0.0821536i	0.427163	+	0.904175i	$0.359513\pi$
$678$		0			0
$679$	−14.6325	−	95.7282i	−0.0215501	−	0.140984i
$680$	−12.9022			−0.0189738
$681$		0			0
$682$	1043.12	+	602.244i	1.52950	+	0.883055i
$683$	−446.238	+	772.907i	−0.653350	+	1.13164i	0.328955	+	0.944346i	$0.393304\pi$
$683$	−446.238	+	772.907i	−0.653350	+	1.13164i	−0.982305	+	0.187290i	$0.940030\pi$
$684$		0			0
$685$		−	16.2018i		−	0.0236523i
$686$	402.486	+	270.745i	0.586715	+	0.394672i
$687$		0			0
$688$	21.5763	+	37.3712i	0.0313609	+	0.0543186i
$689$	−556.828	−	321.485i	−0.808168	−	0.466596i
$690$		0			0
$691$	−393.196	+	227.012i	−0.569025	+	0.328527i	−0.756760	−	0.653693i	$-0.773219\pi$
$691$	−393.196	+	227.012i	−0.569025	+	0.328527i	0.187735	+	0.982220i	$0.439885\pi$
$692$		−	276.258i		−	0.399217i
$693$		0			0
$694$	−43.6698			−0.0629247
$695$	−2.55542	−	4.42612i	−0.00367686	−	0.00636851i
$696$		0			0
$697$	685.466	−	1187.26i	0.983453	−	1.70339i
$698$	636.908	−	367.719i	0.912476	−	0.526818i
$699$		0			0
$700$	−218.321	−	272.600i	−0.311887	−	0.389428i
$701$	−383.121			−0.546536			−0.273268	−	0.961938i	$-0.588105\pi$
$701$	−383.121			−0.546536			−0.273268	+	0.961938i	$0.588105\pi$
$702$		0			0
$703$	381.217	+	220.096i	0.542272	+	0.313081i
$704$	78.2313	−	135.501i	0.111124	−	0.192472i
$705$		0			0
$706$		−	410.645i		−	0.581650i
$707$	−915.876	−	357.257i	−1.29544	−	0.505314i
$708$		0			0
$709$	451.514	+	782.045i	0.636832	+	1.10302i	0.986124	+	0.166011i	$0.0530887\pi$
$709$	451.514	+	782.045i	0.636832	+	1.10302i	−0.349292	+	0.937014i	$0.613578\pi$
$710$	0.731874	+	0.422548i	0.00103081	+	0.000595138i
$711$		0			0
$712$	−105.886	+	61.1335i	−0.148717	+	0.0858616i
$713$		−	235.125i		−	0.329768i
$714$		0			0
$715$	47.2592			0.0660967
$716$	−175.244	−	303.532i	−0.244754	−	0.423927i
$717$		0			0
$718$	186.635	−	323.261i	0.259937	−	0.450224i
$719$	379.783	−	219.268i	0.528210	−	0.304962i	−0.212077	−	0.977253i	$-0.568023\pi$
$719$	379.783	−	219.268i	0.528210	−	0.304962i	0.740287	+	0.672291i	$0.234689\pi$
$720$		0			0
$721$	219.649	−	175.913i	0.304645	−	0.243985i
$722$	−431.296			−0.597362
$723$		0			0
$724$	−562.902	−	324.992i	−0.777489	−	0.448883i
$725$	106.866	−	185.098i	0.147402	−	0.255308i
$726$		0			0
$727$		−	284.851i		−	0.391817i	−0.980622	−	0.195909i	$-0.937234\pi$
$727$		−	284.851i		−	0.391817i	0.980622	−	0.195909i	$-0.0627656\pi$
$728$	−31.2048	−	204.147i	−0.0428638	−	0.280421i
$729$		0			0
$730$	−21.9850	−	38.0791i	−0.0301164	−	0.0521632i
$731$	−183.969	−	106.215i	−0.251668	−	0.145301i
$732$		0			0
$733$	−462.944	+	267.281i	−0.631575	+	0.364640i	−0.781362	−	0.624079i	$-0.785475\pi$
$733$	−462.944	+	267.281i	−0.631575	+	0.364640i	0.149787	+	0.988718i	$0.452141\pi$
$734$		−	356.665i		−	0.485919i
$735$		0			0
$736$	−30.5426			−0.0414981
$737$	714.423	+	1237.42i	0.969366	+	1.67899i
$738$		0			0
$739$	216.551	−	375.077i	0.293032	−	0.507546i	−0.681493	−	0.731824i	$-0.738669\pi$
$739$	216.551	−	375.077i	0.293032	−	0.507546i	0.974525	+	0.224278i	$0.0720024\pi$
$740$	−23.5967	+	13.6235i	−0.0318874	+	0.0184102i
$741$		0			0
$742$	−603.216	+	92.2046i	−0.812960	+	0.124265i
$743$	−300.442			−0.404363			−0.202182	−	0.979348i	$-0.564803\pi$
$743$	−300.442			−0.404363			−0.202182	+	0.979348i	$0.564803\pi$
$744$		0			0
$745$	−38.1433	−	22.0220i	−0.0511991	−	0.0295598i
$746$	304.313	−	527.086i	0.407926	−	0.706549i
$747$		0			0
$748$			770.227i			1.02972i
$749$	783.264	+	977.999i	1.04575	+	1.30574i
$750$		0			0
$751$	574.790	+	995.566i	0.765367	+	1.32565i	0.940052	+	0.341030i	$0.110776\pi$
$751$	574.790	+	995.566i	0.765367	+	1.32565i	−0.174686	+	0.984624i	$0.555891\pi$
$752$	−31.0733	−	17.9402i	−0.0413209	−	0.0238566i
$753$		0			0
$754$	109.452	−	63.1924i	0.145162	−	0.0838095i
$755$		−	20.1879i		−	0.0267390i
$756$		0			0
$757$	1166.13			1.54046			0.770232	−	0.637764i	$-0.220141\pi$
$757$	1166.13			1.54046			0.770232	+	0.637764i	$0.220141\pi$
$758$	−218.291	−	378.091i	−0.287982	−	0.498800i
$759$		0			0
$760$	−2.45227	+	4.24745i	−0.00322667	+	0.00558876i
$761$	−3.11383	+	1.79777i	−0.00409176	+	0.00236238i	−0.502044	−	0.864842i	$-0.667419\pi$
$761$	−3.11383	+	1.79777i	−0.00409176	+	0.00236238i	0.497953	+	0.867204i	$0.334085\pi$
$762$		0			0
$763$	−140.151	+	359.296i	−0.183684	+	0.470899i
$764$	−532.769			−0.697341
$765$		0			0
$766$	287.677	+	166.090i	0.375557	+	0.216828i
$767$	179.748	−	311.332i	0.234352	−	0.405909i
$768$		0			0
$769$		−	979.281i		−	1.27345i	−0.771092	−	0.636724i	$-0.780289\pi$
$769$		−	979.281i		−	1.27345i	0.771092	−	0.636724i	$-0.219711\pi$
$770$	35.0086	−	28.0378i	0.0454658	−	0.0364128i
$771$		0			0
$772$	−304.766	−	527.870i	−0.394774	−	0.683769i
$773$	1028.99	+	594.087i	1.33116	+	0.768547i	0.985478	−	0.169803i	$-0.0543132\pi$
$773$	1028.99	+	594.087i	1.33116	+	0.768547i	0.345685	+	0.938351i	$0.387647\pi$
$774$		0			0
$775$	−940.815	+	543.180i	−1.21395	+	0.700877i
$776$			39.1293i			0.0504243i
$777$		0			0
$778$	−471.423			−0.605942
$779$	−260.568	−	451.316i	−0.334490	−	0.579353i
$780$		0			0
$781$	25.2250	−	43.6909i	0.0322983	−	0.0559423i
$782$	130.210	−	75.1769i	0.166509	−	0.0961342i
$783$		0			0
$784$	−144.232	−	132.715i	−0.183969	−	0.169279i
$785$	−25.7318			−0.0327793
$786$		0			0
$787$	548.690	+	316.786i	0.697192	+	0.402524i	0.806301	−	0.591506i	$-0.201466\pi$
$787$	548.690	+	316.786i	0.697192	+	0.402524i	−0.109109	+	0.994030i	$0.534800\pi$
$788$	209.399	−	362.690i	0.265735	−	0.460267i
$789$		0			0
$790$		−	30.8685i		−	0.0390740i
$791$	−427.880	+	65.4035i	−0.540935	+	0.0826846i
$792$		0			0
$793$	354.217	+	613.522i	0.446680	+	0.773672i
$794$	249.801	+	144.223i	0.314611	+	0.181641i
$795$		0			0
$796$	−211.594	+	122.164i	−0.265821	+	0.153472i
$797$			1013.72i			1.27192i	0.771721	+	0.635962i	$0.219396\pi$
$797$			1013.72i			1.27192i	−0.771721	+	0.635962i	$0.780604\pi$
$798$		0			0
$799$	176.630			0.221064
$800$	70.5589	+	122.212i	0.0881986	+	0.152764i
$801$		0			0
$802$	274.389	−	475.255i	0.342130	−	0.592587i
$803$	−2273.22	+	1312.45i	−2.83091	+	1.63443i
$804$		0			0
$805$	−8.15689	−	3.18177i	−0.0101328	−	0.00395251i
$806$	−642.387			−0.797006
$807$		0			0
$808$	344.009	+	198.614i	0.425754	+	0.245809i
$809$	−480.747	+	832.678i	−0.594248	+	1.02927i	0.399404	+	0.916775i	$0.369217\pi$
$809$	−480.747	+	832.678i	−0.594248	+	1.02927i	−0.993652	+	0.112493i	$0.964116\pi$
$810$		0			0
$811$		−	1543.59i		−	1.90332i	−0.307149	−	0.951661i	$-0.599375\pi$
$811$		−	1543.59i		−	1.90332i	0.307149	−	0.951661i	$-0.400625\pi$
$812$	43.5894	−	111.747i	0.0536816	−	0.137620i
$813$		0			0
$814$	813.289	+	1408.66i	0.999127	+	1.73054i
$815$	−61.0526	−	35.2487i	−0.0749112	−	0.0432500i
$816$		0			0
$817$	−69.9326	+	40.3756i	−0.0855969	+	0.0494194i
$818$			504.240i			0.616431i
$819$		0			0
$820$	32.2573			0.0393382
$821$	−73.7887	−	127.806i	−0.0898767	−	0.155671i	0.817582	−	0.575812i	$-0.195314\pi$
$821$	−73.7887	−	127.806i	−0.0898767	−	0.155671i	−0.907459	+	0.420141i	$0.861981\pi$
$822$		0			0
$823$	2.26701	−	3.92657i	0.00275457	−	0.00477105i	−0.864645	−	0.502384i	$-0.832457\pi$
$823$	2.26701	−	3.92657i	0.00275457	−	0.00477105i	0.867399	+	0.497613i	$0.165790\pi$
$824$	−98.4726	+	56.8532i	−0.119506	+	0.0689966i
$825$		0			0
$826$	−51.5532	−	337.269i	−0.0624131	−	0.408316i
$827$	−1306.91			−1.58030			−0.790152	−	0.612911i	$-0.789998\pi$
$827$	−1306.91			−1.58030			−0.790152	+	0.612911i	$0.789998\pi$
$828$		0			0
$829$	637.227	+	367.903i	0.768669	+	0.443791i	0.832400	−	0.554176i	$-0.186966\pi$
$829$	637.227	+	367.903i	0.768669	+	0.443791i	−0.0637304	+	0.997967i	$0.520300\pi$
$830$	10.9360	−	18.9417i	0.0131759	−	0.0228213i
$831$		0			0
$832$			83.4459i			0.100296i
$833$	941.554	+	210.784i	1.13032	+	0.253042i
$834$		0			0
$835$	0.571914	+	0.990583i	0.000684926	+	0.00118633i
$836$	253.562	+	146.394i	0.303304	+	0.175112i
$837$		0			0
$838$	−622.915	+	359.640i	−0.743335	+	0.429165i
$839$		−	1468.78i		−	1.75063i	−0.483551	−	0.875316i	$-0.660653\pi$
$839$		−	1468.78i		−	1.75063i	0.483551	−	0.875316i	$-0.339347\pi$
$840$		0			0
$841$	−767.594			−0.912716
$842$	−312.765	−	541.724i	−0.371454	−	0.643378i
$843$		0			0
$844$	225.780	−	391.062i	0.267511	−	0.463343i
$845$	12.0775	−	6.97294i	0.0142929	−	0.00825200i
$846$		0			0
$847$	−1144.31	−	1428.81i	−1.35102	−	1.68691i
$848$	246.567			0.290763
$849$		0			0
$850$	−601.618	−	347.344i	−0.707785	−	0.408640i
$851$	158.760	−	274.980i	0.186557	−	0.323126i
$852$		0			0
$853$		−	409.635i		−	0.480228i	−0.970745	−	0.240114i	$-0.922815\pi$
$853$		−	409.635i		−	0.480228i	0.970745	−	0.240114i	$-0.0771849\pi$
$854$	626.386	+	244.335i	0.733473	+	0.286107i
$855$		0			0
$856$	−253.142	−	438.455i	−0.295727	−	0.512214i
$857$	−92.2902	−	53.2838i	−0.107690	−	0.0621747i	0.445188	−	0.895437i	$-0.353137\pi$
$857$	−92.2902	−	53.2838i	−0.107690	−	0.0621747i	−0.552878	+	0.833263i	$0.686470\pi$
$858$		0			0
$859$	−217.146	+	125.369i	−0.252790	+	0.145948i	−0.621041	−	0.783778i	$-0.713290\pi$
$859$	−217.146	+	125.369i	−0.252790	+	0.145948i	0.368251	+	0.929726i	$0.379957\pi$
$860$		−	4.99836i		−	0.00581204i
$861$		0			0
$862$	1181.79			1.37099
$863$	220.851	+	382.525i	0.255911	+	0.443250i	0.965142	−	0.261725i	$-0.0842913\pi$
$863$	220.851	+	382.525i	0.255911	+	0.443250i	−0.709232	+	0.704975i	$0.750958\pi$
$864$		0			0
$865$	−15.9995	+	27.7119i	−0.0184965	+	0.0320369i
$866$	−54.1388	+	31.2570i	−0.0625159	+	0.0360936i
$867$		0			0
$868$	−475.867	+	381.114i	−0.548234	+	0.439072i
$869$	−1842.77			−2.12056
$870$		0			0
$871$	−659.949	−	381.022i	−0.757691	−	0.437453i
$872$	77.9157	−	134.954i	0.0893528	−	0.154764i
$873$		0			0
$874$		−	57.1543i		−	0.0653939i
$875$	12.2382	+	80.0640i	0.0139865	+	0.0915017i
$876$		0			0
$877$	178.466	+	309.112i	0.203496	+	0.352465i	0.949653	−	0.313305i	$-0.101436\pi$
$877$	178.466	+	309.112i	0.203496	+	0.352465i	−0.746156	+	0.665771i	$0.768103\pi$
$878$	−185.249	−	106.954i	−0.210990	−	0.121815i
$879$		0			0
$880$	−15.6950	+	9.06153i	−0.0178353	+	0.0102972i
$881$			856.411i			0.972090i	0.873934	+	0.486045i	$0.161561\pi$
$881$			856.411i			0.972090i	−0.873934	+	0.486045i	$0.838439\pi$
$882$		0			0
$883$	−162.631			−0.184180			−0.0920902	−	0.995751i	$-0.529355\pi$
$883$	−162.631			−0.184180			−0.0920902	+	0.995751i	$0.529355\pi$
$884$	−205.392	−	355.749i	−0.232344	−	0.402431i
$885$		0			0
$886$	308.808	−	534.871i	0.348542	−	0.603692i
$887$	739.068	−	426.701i	0.833222	−	0.481061i	−0.0217325	−	0.999764i	$-0.506918\pi$
$887$	739.068	−	426.701i	0.833222	−	0.481061i	0.854955	+	0.518703i	$0.173585\pi$
$888$		0			0
$889$	−817.526	+	124.963i	−0.919602	+	0.140566i
$890$	14.1622			0.0159126
$891$		0			0
$892$	−48.4435	−	27.9689i	−0.0543089	−	0.0313552i
$893$	33.5714	−	58.1473i	0.0375939	−	0.0651146i
$894$		0			0
$895$			40.5970i			0.0453598i
$896$	49.5066	+	61.8150i	0.0552529	+	0.0689900i
$897$		0			0
$898$	−370.719	−	642.105i	−0.412828	−	0.715039i
$899$	−323.119	−	186.553i	−0.359420	−	0.207511i
$900$		0			0
$901$	−1051.17	+	606.895i	−1.16667	+	0.673579i
$902$		−	1925.68i		−	2.13490i
$903$		0			0
$904$	174.898			0.193471
$905$	37.6437	+	65.2009i	0.0415953	+	0.0720452i
$906$		0			0
$907$	177.344	−	307.168i	0.195528	−	0.338664i	−0.751546	−	0.659681i	$-0.770691\pi$
$907$	177.344	−	307.168i	0.195528	−	0.338664i	0.947073	+	0.321017i	$0.104025\pi$
$908$	315.439	−	182.119i	0.347399	−	0.200571i
$909$		0			0
$910$	−8.69294	+	22.2855i	−0.00955269	+	0.0244896i
$911$	688.935			0.756241			0.378120	−	0.925756i	$-0.376571\pi$
$911$	688.935			0.756241			0.378120	+	0.925756i	$0.376571\pi$
$912$		0			0
$913$	−1130.77	−	652.850i	−1.23852	−	0.715060i
$914$	140.793	−	243.860i	0.154040	−	0.266806i
$915$		0			0
$916$			750.592i			0.819423i
$917$	267.614	−	214.328i	0.291836	−	0.233727i
$918$		0			0
$919$	−121.938	−	211.203i	−0.132685	−	0.229818i	0.792026	−	0.610488i	$-0.209027\pi$
$919$	−121.938	−	211.203i	−0.132685	−	0.229818i	−0.924711	+	0.380670i	$0.875693\pi$
$920$	3.06378	+	1.76887i	0.00333020	+	0.00192269i
$921$		0			0
$922$	828.176	−	478.147i	0.898238	−	0.518598i
$923$			26.9064i			0.0291510i
$924$		0			0
$925$	−1467.05			−1.58600
$926$	236.234	+	409.169i	0.255112	+	0.441867i
$927$		0			0
$928$	−24.2331	+	41.9730i	−0.0261133	+	0.0452296i
$929$	595.349	−	343.725i	0.640849	−	0.369994i	−0.144093	−	0.989564i	$-0.546026\pi$
$929$	595.349	−	343.725i	0.640849	−	0.369994i	0.784941	+	0.619570i	$0.212693\pi$
$930$		0			0
$931$	248.348	−	269.900i	0.266754	−	0.289904i
$932$	35.0301			0.0375859
$933$		0			0
$934$	−798.000	−	460.725i	−0.854390	−	0.493282i
$935$	44.6077	−	77.2628i	0.0477087	−	0.0826340i
$936$		0			0
$937$			354.747i			0.378598i	0.981919	+	0.189299i	$0.0606216\pi$
$937$			354.747i			0.378598i	−0.981919	+	0.189299i	$0.939378\pi$
$938$	−714.928	+	109.280i	−0.762184	+	0.116504i
$939$		0			0
$940$	2.07801	+	3.59922i	0.00221065	+	0.00382895i
$941$	985.712	+	569.101i	1.04752	+	0.604784i	0.921953	−	0.387302i	$-0.126593\pi$
$941$	985.712	+	569.101i	1.04752	+	0.604784i	0.125563	+	0.992086i	$0.459926\pi$
$942$		0			0
$943$	−325.544	+	187.953i	−0.345222	+	0.199314i
$944$			137.860i			0.146038i
$945$		0			0
$946$	−298.389			−0.315422
$947$	511.924	+	886.679i	0.540575	+	0.936303i	0.998871	+	0.0475035i	$0.0151265\pi$
$947$	511.924	+	886.679i	0.540575	+	0.936303i	−0.458296	+	0.888799i	$0.651540\pi$
$948$		0			0
$949$	699.964	−	1212.37i	0.737580	−	1.27753i
$950$	−228.694	+	132.037i	−0.240731	+	0.138986i
$951$		0			0
$952$	−363.208	−	141.677i	−0.381521	−	0.148820i
$953$	−620.107			−0.650690			−0.325345	−	0.945595i	$-0.605480\pi$
$953$	−620.107			−0.650690			−0.325345	+	0.945595i	$0.605480\pi$
$954$		0			0
$955$	53.4429	+	30.8553i	0.0559611	+	0.0323092i
$956$	−249.150	+	431.541i	−0.260618	+	0.451403i
$957$		0			0
$958$		−	211.805i		−	0.221091i
$959$	177.910	−	456.095i	0.185516	−	0.475595i
$960$		0			0
$961$	467.708	+	810.093i	0.486688	+	0.842969i
$962$	−751.276	−	433.750i	−0.780952	−	0.450883i
$963$		0			0
$964$	−108.084	+	62.4023i	−0.112120	+	0.0647327i
$965$			70.6020i			0.0731627i
$966$		0			0
$967$	718.914			0.743448			0.371724	−	0.928343i	$-0.378767\pi$
$967$	718.914			0.743448			0.371724	+	0.928343i	$0.378767\pi$
$968$	369.829	+	640.563i	0.382055	+	0.661739i
$969$		0			0
$970$	2.26617	−	3.92512i	0.00233626	−	0.00404652i
$971$	−631.818	+	364.780i	−0.650688	+	0.375675i	−0.788720	−	0.614753i	$-0.789256\pi$
$971$	−631.818	+	364.780i	−0.650688	+	0.375675i	0.138032	+	0.990428i	$0.455922\pi$
$972$		0			0
$973$	−23.3348	−	152.660i	−0.0239823	−	0.156896i
$974$	1274.31			1.30832
$975$		0			0
$976$	−235.275	−	135.836i	−0.241060	−	0.139176i
$977$	−784.316	+	1358.48i	−0.802780	+	1.39046i	0.115000	+	0.993366i	$0.463313\pi$
$977$	−784.316	+	1358.48i	−0.802780	+	1.39046i	−0.917780	+	0.397090i	$0.870020\pi$
$978$		0			0
$979$		−	845.444i		−	0.863579i
$980$	6.78197	+	21.6660i	0.00692037	+	0.0221082i
$981$		0			0
$982$	−178.377	−	308.959i	−0.181647	−	0.314622i
$983$	−1305.58	−	753.777i	−1.32816	−	0.766813i	−0.343144	−	0.939283i	$-0.611492\pi$
$983$	−1305.58	−	753.777i	−1.32816	−	0.766813i	−0.985015	+	0.172470i	$0.944825\pi$
$984$		0			0
$985$	−42.0104	+	24.2547i	−0.0426502	+	0.0246241i
$986$		−	238.588i		−	0.241975i
$987$		0			0
$988$	−156.152			−0.158048
$989$	29.1238	+	50.4439i	0.0294477	+	0.0510050i
$990$		0			0
$991$	250.882	−	434.540i	0.253160	−	0.438487i	−0.711234	−	0.702956i	$-0.751863\pi$
$991$	250.882	−	434.540i	0.253160	−	0.438487i	0.964394	+	0.264469i	$0.0851966\pi$
$992$	213.340	−	123.172i	0.215060	−	0.124165i
$993$		0			0
$994$	15.9630	+	19.9317i	0.0160593	+	0.0200520i
$995$	28.3004			0.0284426
$996$		0			0
$997$	−765.965	−	442.230i	−0.768269	−	0.443561i	0.0639875	−	0.997951i	$-0.479618\pi$
$997$	−765.965	−	442.230i	−0.768269	−	0.443561i	−0.832257	+	0.554390i	$0.812952\pi$
$998$	205.546	−	356.016i	0.205958	−	0.356729i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.n.c.325.5	yes	12
3.2	odd	2		378.3.n.e.325.2	yes	12
7.5	odd	6	inner	378.3.n.c.271.5	✓	12
21.5	even	6		378.3.n.e.271.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.3.n.c.271.5	✓	12	7.5	odd	6	inner
378.3.n.c.325.5	yes	12	1.1	even	1	trivial
378.3.n.e.271.2	yes	12	21.5	even	6
378.3.n.e.325.2	yes	12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.200623 - 0.115830i) q^{5} +(6.91963 - 1.05770i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.200623 - 0.115830i) q^{5} +(6.91963 - 1.05770i) q^{7} -2.82843 q^{8} +(0.283724 + 0.163808i) q^{10} +(9.77891 - 16.9376i) q^{11} +10.4307i q^{13} +(6.18833 + 7.72687i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(17.0529 + 9.84551i) q^{17} +(6.48236 - 3.74259i) q^{19} +0.463320i q^{20} +27.6589 q^{22} +(-2.69961 - 4.67587i) q^{23} +(-12.4732 + 21.6042i) q^{25} +(-12.7750 + 7.37564i) q^{26} +(-5.08764 + 13.0428i) q^{28} -8.56771 q^{29} +(37.7135 + 21.7739i) q^{31} +(2.82843 - 4.89898i) q^{32} +27.8473i q^{34} +(1.26573 - 1.01370i) q^{35} +(29.4042 + 50.9296i) q^{37} +(9.16744 + 5.29282i) q^{38} +(-0.567448 + 0.327616i) q^{40} -69.6222i q^{41} -10.7881 q^{43} +(19.5578 + 33.8752i) q^{44} +(3.81783 - 6.61267i) q^{46} +(7.76832 - 4.48504i) q^{47} +(46.7625 - 14.6378i) q^{49} -35.2794 q^{50} +(-18.0666 - 10.4307i) q^{52} +(-30.8209 + 53.3834i) q^{53} -4.53076i q^{55} +(-19.5717 + 2.99162i) q^{56} +(-6.05829 - 10.4933i) q^{58} +(-29.8476 - 17.2325i) q^{59} +(58.8187 - 33.9590i) q^{61} +61.5860i q^{62} +8.00000 q^{64} +(1.20819 + 2.09265i) q^{65} +(-36.5287 + 63.2696i) q^{67} +(-34.1058 + 19.6910i) q^{68} +(2.13653 + 0.833397i) q^{70} +2.57953 q^{71} +(-116.231 - 67.1059i) q^{73} +(-41.5838 + 72.0253i) q^{74} +14.9704i q^{76} +(49.7516 - 127.545i) q^{77} +(-47.1107 - 81.5982i) q^{79} +(-0.802493 - 0.463320i) q^{80} +(85.2695 - 49.2304i) q^{82} -66.7610i q^{83} +4.56162 q^{85} +(-7.62837 - 13.2127i) q^{86} +(-27.6589 + 47.9067i) q^{88} +(37.4365 - 21.6140i) q^{89} +(11.0326 + 72.1768i) q^{91} +10.7984 q^{92} +(10.9861 + 6.34281i) q^{94} +(0.867008 - 1.50170i) q^{95} -13.8343i q^{97} +(50.9936 + 46.9217i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 6 q^{5}+O(q^{10}) \) 12 * q - 12 * q^4 - 6 * q^5	\( 12 q - 12 q^{4} - 6 q^{5} - 12 q^{10} + 6 q^{11} - 12 q^{14} - 24 q^{16} + 24 q^{17} - 30 q^{19} + 96 q^{23} + 36 q^{25} - 48 q^{26} + 24 q^{28} - 108 q^{29} + 36 q^{31} + 108 q^{35} - 12 q^{37} + 96 q^{38} + 24 q^{40} - 156 q^{43} + 12 q^{44} + 48 q^{46} - 42 q^{47} - 108 q^{49} - 336 q^{50} + 48 q^{52} - 60 q^{53} + 24 q^{56} + 12 q^{58} + 66 q^{59} + 186 q^{61} + 96 q^{64} + 180 q^{65} - 156 q^{67} - 48 q^{68} - 72 q^{70} - 372 q^{71} - 366 q^{73} + 24 q^{74} + 534 q^{77} + 84 q^{79} + 24 q^{80} - 192 q^{82} + 276 q^{85} + 12 q^{86} + 306 q^{89} + 390 q^{91} - 384 q^{92} + 24 q^{94} - 420 q^{95} + 216 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 - 6 * q^5 - 12 * q^10 + 6 * q^11 - 12 * q^14 - 24 * q^16 + 24 * q^17 - 30 * q^19 + 96 * q^23 + 36 * q^25 - 48 * q^26 + 24 * q^28 - 108 * q^29 + 36 * q^31 + 108 * q^35 - 12 * q^37 + 96 * q^38 + 24 * q^40 - 156 * q^43 + 12 * q^44 + 48 * q^46 - 42 * q^47 - 108 * q^49 - 336 * q^50 + 48 * q^52 - 60 * q^53 + 24 * q^56 + 12 * q^58 + 66 * q^59 + 186 * q^61 + 96 * q^64 + 180 * q^65 - 156 * q^67 - 48 * q^68 - 72 * q^70 - 372 * q^71 - 366 * q^73 + 24 * q^74 + 534 * q^77 + 84 * q^79 + 24 * q^80 - 192 * q^82 + 276 * q^85 + 12 * q^86 + 306 * q^89 + 390 * q^91 - 384 * q^92 + 24 * q^94 - 420 * q^95 + 216 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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